Theproduct ruleprovides a way to countntuples created from pairing items in sets.

In contrast, thesum ruleis applied when there are multiple choices from different setsbut only one selection is made.

1.Passwords

Each character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid passwords are there with the given restriction(s)?

• Length is 15
• Cannot startwith a digit.
• Cannot end with a digit.

is it?

26²36¹³

10²36¹³

26²+36¹³

or 10²+36¹³

r-Permutations

Anr-permutationis a sequence of r items with no repetitions, all taken from the same set

2 Recruitment Team.

A group of 14 department heads needs to come up with a search team to look for the company's next CEO. This team is made up of:

1. Team leader
2. A Chairperson,
3. An assistant chairperson,
4. A contact person
5. A secretary.

How many ways are there to select the members of the search team?

145=70

C(14,5)=2002

P(14,5)=240240

14⁵=537824